Exam 5: Network Models

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In a typical network model representation of the transportation problem, the nodes indicate

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Exhibit 5-2A small engineering firm employs one civil engineer, two engineering technicians, and one summer intern. The types of projects the firm does includes surveys (typically 7 per month), designs (5 per month), and construction project plans (four per month). The times, in hours, required for each employee to complete teach type of project are shown below. Based on their capabilities and time spent on travel and administrative tasks, the engineer, tech 1, tech 2, and intern can handle 5, 4, 4, and 3 projects per month, respectively. Exhibit 5-2A small engineering firm employs one civil engineer, two engineering technicians, and one summer intern. The types of projects the firm does includes surveys (typically 7 per month), designs (5 per month), and construction project plans (four per month). The times, in hours, required for each employee to complete teach type of project are shown below. Based on their capabilities and time spent on travel and administrative tasks, the engineer, tech 1, tech 2, and intern can handle 5, 4, 4, and 3 projects per month, respectively.    -Refer to Exhibit 5-2. Implement a LP model in Solver and determine the optimal monthly assignment plan for the firm. What is the total number of hours that will be assigned to projects each month? -Refer to Exhibit 5-2. Implement a LP model in Solver and determine the optimal monthly assignment plan for the firm. What is the total number of hours that will be assigned to projects each month?

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In transportation problems, the three sets of input numbers that are required are capacities, demands and flows.

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Exhibit 5-2A small engineering firm employs one civil engineer, two engineering technicians, and one summer intern. The types of projects the firm does includes surveys (typically 7 per month), designs (5 per month), and construction project plans (four per month). The times, in hours, required for each employee to complete teach type of project are shown below. Based on their capabilities and time spent on travel and administrative tasks, the engineer, tech 1, tech 2, and intern can handle 5, 4, 4, and 3 projects per month, respectively. Exhibit 5-2A small engineering firm employs one civil engineer, two engineering technicians, and one summer intern. The types of projects the firm does includes surveys (typically 7 per month), designs (5 per month), and construction project plans (four per month). The times, in hours, required for each employee to complete teach type of project are shown below. Based on their capabilities and time spent on travel and administrative tasks, the engineer, tech 1, tech 2, and intern can handle 5, 4, 4, and 3 projects per month, respectively.    -Refer to Exhibit 5-2. Suppose Tech 2 will not be available during the next month. Keeping the same number of design and construction plan projects, how many survey projects would the firm be able to do? What would be the revised assignment plan in that case? -Refer to Exhibit 5-2. Suppose Tech 2 will not be available during the next month. Keeping the same number of design and construction plan projects, how many survey projects would the firm be able to do? What would be the revised assignment plan in that case?

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Exhibit 5-1Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below: Exhibit 5-1Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below:    -Refer to Exhibit 5-1. Suppose the Lakeview plant was required to run at capacity. How much more would the shipping plan cost Sinclair? -Refer to Exhibit 5-1. Suppose the Lakeview plant was required to run at capacity. How much more would the shipping plan cost Sinclair?

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The objective in transportation problems is typically to:

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In an optimized shipping plan, most of the shipments occur on the low-cost routes, but this is not always the case.

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The cost of an arc in a shortest path problem is equal to the distance of the arc.

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The graphical representation of a network in an optimization problem can be an aid in the development of a spreadsheet model.

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A typical shortest path problem is a special case of the general network flow model.

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